Since I just made mention of Science News in my response to Scoble’s comment on my blog entry about tech blogs all drinking at the same watering hole, I thought I’d point to an actual Science News story that might be of interest to the Radar audience: Math Trek: A Tangled Tale. Go read that article, about an experiment by Dorian Raymer and Douglas Smith at the University of California, San Diego, tumbling lengths of string into knots, and tell me you didn’t learn more than you did from a story about one more me-too Web 2.0 startup….
A few tidbits:
- It takes only ten turns for a typical length of string tumbled at random to form a knot.
-
For purposes of mathematical analysis, mathematicians create an “ideal form” of the knot by connecting its ends. Two knots are considered equivalent if you can transform one into another simply by moving the string around without cutting it.
Although these three knots look quite unalike, they’re all really just simple loops with no actual knots, meaning that each one can be pulled into a simple loop without cutting the string. Mathematicians call this the "unknot."
Wikipedia, via Science News - “Back in 1983, a mathematician named Vaughan Jones at the University of California, Berkeley devised a mathematical expression—now known as the Jones polynomial—that can be defined for any knot. The remarkable thing is that if two knots are equivalent, they’ll each yield the same Jones polynomial. It’s not a perfect way to classify all knots, because some complicated knots that aren’t equivalent correspond to the same polynomial—so knot theorists still have plenty to keep them busy.”
- A knot is considered “prime” if it can’t be decomposed into two simpler knots. All of the knots generated by the tumbling experiment were prime.
Now, I’m waiting for the practical application: a headset for my phone that doesn’t tie itself into knots. (And no, I don’t want bluetooth. Having to remember to recharge another device is the only thing worse than untangling the headset cord. Universal recharging anyone? Mobilewise promised this back in 2002, but it never caught on.)